The deal was first reported by German business newspaper Handelsblatt, which quoted government sources.
The government in 2004 sought damages from Toll Collect - which is 45 percent-owned by German carmaker Daimler, 45 percent by Deutsche Telekom and 10 percent by Vinci unit Cofiroute - over delays to the introduction of the world's first satellite-based truck toll system.
Handelsblatt said that under the deal, which still needs court approval, the government would receive 1.1 billion euros from Toll Collect. That figure was later confirmed by Daimler in a statement.
Handelsblatt said the government would in addition keep 1.136 billion euros in arrears. The consortium will also pay about one billion euros in interest and penalties for breach of contract.
Daimler said in a statement the deal could lead to a one-off negative impact on earnings before interest and tax (EBIT) of 600 million euros in its results for the current quarter.
Telekom said in its statement that it would make a one-time final payment of 550 million euros under the settlement.
It added that board members of Daimler and Telekom held intensive negotiations with the government to end the 14-year dispute after the arbitration tribunal was unable to reach a decision.
"Deutsche Telekom examined the risks and opportunities associated with further pursuit of the arbitration process extensively, from both a legal and business perspective, and believes that the settlement is the best possible solution," said Telekom board member Thomas Kremer.
Transport Minister Andreas Scheuer told Handelsblatt that the deal was a "historic break through."
The German government said earlier this year it planned to nationalise Toll Collect temporarily until a new operator had been found.
The federal government intends to take over Toll Collect in September before starting the bidding process to renew the operating contract, which expires this year.
(Reporting by Joseph Nasr; Editing by Mark Potter)